Jamieson, Fausset and Brown on 1 Chronicles 16:36

36. all the people said, Amen--(Compare Psa 72:19, 20; 106:48). In the former, the author of the doxology utters the "amen" himself, while in the latter the people are exhorted to say "amen." This may arise from the fact that the latter psalm originally concluded with the injunction to say "amen." But in this historical account of the festival, it was necessary to relate that the people obeyed this injunction on the occasion referred to, and therefore the words "let them praise," were altered into "and they praised" [Bertheau].